You will have heard of Bob Crow, who some call Satan, Beelzebub, the Skinhead of Woodford or, when bestowing a fuller title, "That Bastard Bob Crow". He's the cockney boss of the Rail, Maritime and Transport Workers union, which is the least accommodating of the three that represent London Underground workers and has just drawn back from, oh, an eternity of strikes over the dismissal of two of its members – the unfair dismissal in at least one case. For now, then, the capital has been spared its 22nd withdrawal of RMT labour in the past three years, but its citizens had already been reinformed of the alleged cost of such action to the metropolis.

This traditionally takes the form of a nice round number: £50m a day. It comes in handy for time-coshed journalists and was recently cited by Esher and Walton MP Dominic Raab, who wants the law changed to make it harder for Satan to work his "Soviet-style" devilry. But where does that £50m figure come from? Human resources journal Personnel Today has found its source to be a survey by the London Chamber of Commerce and Industry conducted four years ago. Cisco's HR chief told Personnel Today that she'd be "hugely surprised" if the damage was still at such a level, as collaborative technology has grown.

How disruptive to the underground system are the strikes anyway? Bosses and union, naturally, never agree but my observations of recent picket line scenes suggest there's more bark from Bob than there is bite. Parts of the network close down, especially in the mornings, and others are slowed but there's nowhere you can't get to with the help of a bus, a bicycle or shoe leather. Boris Johnson takes a similar line. In January he told a London Assembly member that "in many cases" strikes have had "little or no impact on services".

The almighty fuss is not about profits, but pride, publicity and passing the buck. With an election just a year away, Johnson's record on transport is patchy and there have been more tube strikes since he took power in 2008 than in the whole of Ken Livingstone's preceding eight years. Johnson claims that his predecessor was an appeasing pushover, a view not really shared by Crow and his lieutenants, who fell out badly with Livingstone and were alone among tube unions in not backing his campaign to become Labour's candidate for 2012.

The present mayor has long been asking the government to supply the legislation Raab demanded and lately called its lack of progress "lily-livered". The Financial Times told him to "simmer down" – the government can only lose from appearing to embark on an "anti-union crusade", it said; and government minsters have told him to "get off his backside" and change his policy of doing precisely nothing to build some sort of relationship with Crow and co. But that's how it is with Mayor Jolly Good-Fun: when the going gets tough, he goes off to pose for pictures with policemen.

The truth is that tube strikes, while a pain for passengers and an embarrassment for all London mayors, are not the dire threat to the prosperity of the "engine of the UK economy" they are depicted as. If you want to bandy estimates, then try the £2bn a year that a report for London First, the body representing the capital's biggest employers, reckons the capital loses due to road congestion every year. The mayor's own transport strategy doubles that to a massive £4bn, yet he's halved the size of the congestion charging zone and brought traffic flow measures whose impact so far has been at best minute.

The RMT is a stroppy outfit with a bruisingly basic commitment to looking after its own. I'm sure it's hell to live with. But if the mayor wants to make the wheels of capitalism turn more smoothly on his patch, he needs to tackle some much bigger enemies.